Question: Factor completely. $49m^2-126mn+81n^2=$
Explanation: $\begin{aligned} &\phantom{=}49 m ^2 - 126 m n + 81 n ^2 \\\\ &= ({7 m })^2 - 2({7 m })({9 n })+({9 n })^2 \end{aligned}$ Using the square of a difference pattern: $\begin{aligned} &\phantom{=}({7 m })^2 - 2({7 m })({9 n })+({9 n })^2 \\\\ &=({7 m } - {9 n })^2 \end{aligned}$ In conclusion, $49 m ^2 - 126 m n + 81 n ^2=(7 m - 9 n )^2$ Remember that you can always check your factorization by expanding it.